The Kavanagh opinion absolutely does mention Title IX, and it notes that with direct compensation from schools that question would need to be squared with litigation, legislation, or collective bargaining. The route taken for starters was litigation + settlement. In that settlement, there were no restrictions on who would get paid what money, the schools were effectively free to do whatever they wanted within the cap. And, most importantly, the backpay part of the settlement is more-or-less earmarked for football stars... there is a claims process that is expected to pay out up to $1.85 million max to a former player out of a $2.8 billion pool, and the amount you get is based on things (generally) tied to the revenue/ratings/etc. you produced.
Very clearly in the intent of the claims process from that settlement -- a field hockey player from Duke is not going to get the same payout as a football player from Bama.
Then, seemingly out of nowhere, the DoE decrees that women need to receive equal revenue ... not just from the cap and settlement, but also potentially from 3rd party NIL ... the latter part of that being batshit insane and completely misaligned with the O'Bannon case, Alston case, NCAA NIL rules, and the House settlement. They're trying to legislate swimmers with no Q score getting the same 3rd party money as Arch Manning and his cohorts, and that's bonkers level absurd.